Structure formation in the presence of dark energy perturbations

We study non-linear structure formation in the presence of dark energy. The influence of dark energy on the growth of large-scale cosmological structures is exerted both through its background effect on the expansion rate, and through its perturbations. In order to compute the rate of formation of massive objects we employ the spherical collapse formalism, which we generalize to include fluids with pressure. We show that the resulting non-linear evolution equations are identical to the ones obtained in the pseudo-Newtonian approach to cosmological perturbations, in the regime where an equation of state serves to describe both the background pressure relative to density, and the pressure perturbations relative to the density perturbations. We then consider a wide range of constant and time-dependent equations of state (including phantom models) parametrized in a standard way, and study their impact on the non-linear growth of structure. The main effect is the formation of dark energy structure associated with the dark matter halo: non-phantom equations of state induce the formation of a dark energy halo, damping the growth of structures; phantom models, on the other hand, generate dark energy voids, enhancing structure growth. Finally, we employ the Press-Schechter formalism to compute how dark energy affects the number of massive objects as a function of redshift (number counts).